Mathematics – Functional Analysis
Scientific paper
2011-02-21
Mathematics
Functional Analysis
Some corrections and clarifications. To appear in Linear Algebra and its Applications
Scientific paper
It is well-known that if T is a D_m-D_n bimodule map on the m by n complex matrices, then T is a Schur multiplier and $\|T\|_{cb}=\|T\|$. If n=2 and T is merely assumed to be a right D_2-module map, then we show that $\|T\|_{cb}=\|T\|$. However, this property fails if m>1 and n>2. For m>1 and n=3,4 or $n\geq m^2$, we give examples of maps T attaining the supremum C(m,n)=\sup \|T\|_{cb} taken over the contractive, right D_n-module maps on M_{m,n}, we show that C(m,m^2)=\sqrt{m} and succeed in finding sharp results for C(m,n) in certain other cases. As a consequence, if H is an infinite-dimensional Hilbert space and D is a masa in B(H), then there is a bounded right D-module map on the compact operators K(H) which is not completely bounded.
Levene Rupert H.
Timoney Richard M.
No associations
LandOfFree
Completely bounded norms of right module maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Completely bounded norms of right module maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Completely bounded norms of right module maps will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-520892